《电动力学》课程参考文献：High-Impedance Electromagnetic Surfaces with a Forbidden Frequency Band

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL 47, NO. 11, NOVEMBER 1999 High-Impedance Electromagnetic Surfaces with a Forbidden Frequency Band Dan Sievenpiper, Member, IEEE, Lijun Zhang, Romulo F Jimenez Broas, Nicholas G. Alexopolous, Fellow, IEEE, and Eli Yablonovitch, Fellow, IEEE Abstract-A new type of metallic electromagnetic structure has been developed that is characterized by having high sur- ■匚匚匚匚匚E face impedance. Although it is made of continuous metal, and conducts de currents, it does not conduct ac currents within a forbidden frequency band. Unlike normal conductors, this new surface does not support propagating surface waves, and its image currents are not phase reversed. The geometry is analogous to a corrugated metal surface in which the corrugations have been folded up into lumped-circuit elements, and distributed in a two-dimensional lattice. The surface can be described using solid-state band theory concepts, even though the periodicity is much less than the free-space wavelength. This unique material is applicable to a variety of electromagnetic problems, including new kinds of low-profile antennas Index Terms- Antennas, corrugated surfaces, photonic bandgap, surface impedance, surface waves, textured surfaces. L. INTRODUCTION A. Electric Con A FLAT METAL sheet is used in many reflector or ground plane [1]. The presence of a ground Fig. I. (a) cross section of a high-impedance surface, fabricated asar plane redirects one-half of the radiation into the opposite to a solid metal sheet by vertical conducting vias. (b)Top view direction, improving the antenna gain by 3 dB, and partially high-impedance surface, showing a triangular lattice of hexagonal metal shielding objects on the other side. If the antenna is too close to the conductive surface, the image currents cancel the currents vertically if scattered by bends, discontinuities, or surface the antenna, resulting in poor radiation efficiency. This texture problem is often addressed by including a quarter-wavelength Surface waves appear in many situations involving antennas space between the radiating element and the ground plane, but On a finite ground plane, surface waves propagate until they such a structure then requires a minimum thickness of A/4. reach an edge or corner, where they can radiate into free space Another property of metals is that they support surface The result is a kind of multipath interference or"speckle, waves [21, [3]. These are propagating electromagnetic waves which can be seen as ripples in the radiation pattern. Moreover, that are bound to the interface between metal and free space. if multiple antennas share the same ground plane, surface They are called surface plasmons at optical frequencies [4], currents can cause unwanted mutual coupling but at microwave frequencies, they are nothing more than the normal currents that occur on any electric conductor. If the B. High-Impedance Surfaces metal surface is smooth and flat, the surface waves will not By incorporating a special texture on a conducting surface couple to external plane waves. However, they will radiate it is possible to alter its radio-frequency electromagnetic Manuscript received March 8, 1999, revised July 9, 1999. This work was properties [5],[6). In the limit where the period of the surface ported by the Army Research Office under Grant DAAHo4-96-1-0389, by texture is much smaller than the wavelength, the structure IRL Laboratories under Subcontract SI-602680-1, and by the Office of Naval can be described using an effective medium model, and its Research under Grant No0014-99-1-013 qualities can be summarized into a single parameter: the L ZhangrF.J. Broas, and E. Yablonovitch are with the Electrical En- surface impedance. A smooth conducting sheet has low surface ineering Department, University of California at Los Angeles, Los Angeles, impedance, but with a specially designed geometry, a textured surface can have high surface im Engineering, University of Califomia at Irvine, Irvine, CA 92697 USA An example of a high-impedance surface, shown in Fig. I Publisher Item Identifier S 0018-9480(99)08780-3 consists of an array of metal protrusions on a flat metal sheet 001894809910.00@1999IEEE

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 47, NO. 11, NOVEMBER 1999 2059 High-Impedance Electromagnetic Surfaces with a Forbidden Frequency Band Dan Sievenpiper, Member, IEEE, Lijun Zhang, Romulo F. Jimenez Broas, Nicholas G. Alexopolous, ´ Fellow, IEEE, and Eli Yablonovitch, Fellow, IEEE Abstract— A new type of metallic electromagnetic structure has been developed that is characterized by having high sur￾face impedance. Although it is made of continuous metal, and conducts dc currents, it does not conduct ac currents within a forbidden frequency band. Unlike normal conductors, this new surface does not support propagating surface waves, and its image currents are not phase reversed. The geometry is analogous to a corrugated metal surface in which the corrugations have been folded up into lumped-circuit elements, and distributed in a two-dimensional lattice. The surface can be described using solid-state band theory concepts, even though the periodicity is much less than the free-space wavelength. This unique material is applicable to a variety of electromagnetic problems, including new kinds of low-profile antennas. Index Terms— Antennas, corrugated surfaces, photonic bandgap, surface impedance, surface waves, textured surfaces. I. INTRODUCTION A. Electric Conductors AFLAT METAL sheet is used in many antennas as a reflector or ground plane [1]. The presence of a ground plane redirects one-half of the radiation into the opposite direction, improving the antenna gain by 3 dB, and partially shielding objects on the other side. If the antenna is too close to the conductive surface, the image currents cancel the currents in the antenna, resulting in poor radiation efficiency. This problem is often addressed by including a quarter-wavelength space between the radiating element and the ground plane, but such a structure then requires a minimum thickness of . Another property of metals is that they support surface waves [2], [3]. These are propagating electromagnetic waves that are bound to the interface between metal and free space. They are called surface plasmons at optical frequencies [4], but at microwave frequencies, they are nothing more than the normal currents that occur on any electric conductor. If the metal surface is smooth and flat, the surface waves will not couple to external plane waves. However, they will radiate Manuscript received March 8, 1999; revised July 9, 1999. This work was supported by the Army Research Office under Grant DAAH04-96-1-0389, by HRL Laboratories under Subcontract S1-602680-1, and by the Office of Naval Research under Grant N00014-99-1-0136. D. Sievenpiper is with HRL Laboratories, Malibu, CA 90265 USA. L. Zhang, R. F. J. Broas, and E. Yablonovitch are with the Electrical En￾gineering Department, University of California at Los Angeles, Los Angeles, CA 90095 USA. N. G. Alexopolous is with the Department of Electrical and Computer ´ Engineering, University of California at Irvine, Irvine, CA 92697 USA. Publisher Item Identifier S 0018-9480(99)08780-3. (a) (b) Fig. 1. (a) Cross section of a high-impedance surface, fabricated as a printed circuit board. The structure consists of a lattice of metal plates, connected to a solid metal sheet by vertical conducting vias. (b) Top view of the high-impedance surface, showing a triangular lattice of hexagonal metal plates. vertically if scattered by bends, discontinuities, or surface texture. Surface waves appear in many situations involving antennas. On a finite ground plane, surface waves propagate until they reach an edge or corner, where they can radiate into free space. The result is a kind of multipath interference or “speckle,” which can be seen as ripples in the radiation pattern. Moreover, if multiple antennas share the same ground plane, surface currents can cause unwanted mutual coupling. B. High-Impedance Surfaces By incorporating a special texture on a conducting surface, it is possible to alter its radio-frequency electromagnetic properties [5], [6]. In the limit where the period of the surface texture is much smaller than the wavelength, the structure can be described using an effective medium model, and its qualities can be summarized into a single parameter: the surface impedance. A smooth conducting sheet has low surface impedance, but with a specially designed geometry, a textured surface can have high surface impedance. An example of a high-impedance surface, shown in Fig. 1, consists of an array of metal protrusions on a flat metal sheet. 0018–9480/99$10.00  1999 IEEE

2060 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL, 47, NO Il, NOVEMBER 1999 They are arranged in a two-dimensional visualized as mushrooms or thumbtacks ng from the surface. The structure is easily fabricated board technology. The protrusions are formed as metal patches on the top surface of the board, connected to the solid lower conducting surface by metal plated vias If the protrusions are small compared to the operating wave- length, their electromagnetic properties can be described using Fig. 2. Surface wave bound to a dielectric interface, decaying exponentially lumped-circuit elements--capacitors and inductors. They be- away from the surface ive as a network of parallel resonant LC circuits, which act as a two-dimensional electric filter to block the flow of surface impedance is very high, the tangential magnetic field solved to obtain the following results / .equations can be currents along the sheet. In the frequency range where the or the waves described above. maxwells is small, even with a large electric field along the surface. Such a structure is sometimes described as a"magnetic conductor V1+E Due to this unusual boundary condition, the high-impedance surface can function as a unique new type of ground plane for low-profile antennas. The image currents are in-phase, rather adjacent to the surface, while still radiating efficiently, F o. than out-of-phase, allowing radiating elements to lie direct 1+eC (5) xample, a dipole lying flat against a high-impedance ground If e is positive then a and y are imaginary, and the waves plane is not shorted out as it would be on an ordinary metal do not decay with distance from the surface; they are simply sheet. Furthermore,in a forbidden frequency band, the high- plane waves propagating through the dielectric interface. Thus, impedance ground plane does not support propagating surface TM surface waves do not exist on nonconductive dielectric waves,thus, the radiation pattern is typically smooth, and free materials. On the other hand. if E is less than -1. or if it rom the effects of multipath interference along the ground is imaginary, the solution describes a wave that is bound to the surface. These TM surface waves can occur on metals or other materials with nonpositive dielectric constants. The IL. SURFACE WAVES solution for te surface waves can also be obtained from the foregoing analysis by the principle of duality [1]. If the electric dissimilar materials, such as metal and free space. They are the solution above can be applied to the le case uted for E, Surface waves can occur on the interface between two and magnetic fields are exchanged, and u is substituted for e bound to the interface, and decay exponentially into the sur- rounding materials. At radio frequencies, the fields associated B. Metal Surfaces with these waves can extend thousands of wavelengths into the surrounding space, and they are often best described as surface The effective. relative dielectric constant of a metal can be currents. They can be modeled from the viewpoint of an expressed in the following form [71 effective dielectric constant, or an effective surface impedance A. Dielectric Interfaces o is the conductivity, which is given by the following equation To derive the properties of surface waves on a dielectric interface [3],[7], begin with a surface in the Y Z plane, as X>0is filled with 1+ while the region X <0 is filled with dielectric E. Assume T is the mean electron collision time, q is the electron a wave that is bound to the surface, decaying in the +X- charge, and m and n are the effective mass and the density, direction with decay constant a, and in the -X-direction with respectively, of the conduction electrons decay constant y. The wave propagates in the Z-direction with For frequencies much lower than 1/ T, including the mi- propagation constant k. For a TM polarized surface wave, crowave spectrum, the conductivity is primarily real, and much Ey=0. The electric field in the upper half-space has the greater than unity, thus, the dielectric constant is a large following form imaginary number. Inserting (6) into(3)leads to a simple dispersion relation for surface waves at radio frequencies En=(iELr + 2El)eJu (1)follows In the lower half-space, the electric field has a similar form as follows: Thus, surface waves propagate at nearly the speed of light in vacuum, and they travel for many wavelengths along the metal E2=(E2x+2E2 ahaz+a (2) surface with little attenuation. By inserting()into(4),we can

2060 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 47, NO. 11, NOVEMBER 1999 They are arranged in a two-dimensional lattice, and can be visualized as mushrooms or thumbtacks protruding from the surface. The structure is easily fabricated using printed-circuit￾board technology. The protrusions are formed as metal patches on the top surface of the board, connected to the solid lower conducting surface by metal plated vias. If the protrusions are small compared to the operating wave￾length, their electromagnetic properties can be described using lumped-circuit elements—capacitors and inductors. They be￾have as a network of parallel resonant circuits, which act as a two-dimensional electric filter to block the flow of currents along the sheet. In the frequency range where the surface impedance is very high, the tangential magnetic field is small, even with a large electric field along the surface. Such a structure is sometimes described as a “magnetic conductor.” Due to this unusual boundary condition, the high-impedance surface can function as a unique new type of ground plane for low-profile antennas. The image currents are in-phase, rather than out-of-phase, allowing radiating elements to lie directly adjacent to the surface, while still radiating efficiently. For example, a dipole lying flat against a high-impedance ground plane is not shorted out as it would be on an ordinary metal sheet. Furthermore, in a forbidden frequency band, the high￾impedance ground plane does not support propagating surface waves, thus, the radiation pattern is typically smooth, and free from the effects of multipath interference along the ground plane. II. SURFACE WAVES Surface waves can occur on the interface between two dissimilar materials, such as metal and free space. They are bound to the interface, and decay exponentially into the sur￾rounding materials. At radio frequencies, the fields associated with these waves can extend thousands of wavelengths into the surrounding space, and they are often best described as surface currents. They can be modeled from the viewpoint of an effective dielectric constant, or an effective surface impedance. A. Dielectric Interfaces To derive the properties of surface waves on a dielectric interface [3], [7], begin with a surface in the plane, as shown in Fig. 2. The region is filled with vacuum, while the region is filled with dielectric . Assume a wave that is bound to the surface, decaying in the - direction with decay constant , and in the -direction with decay constant . The wave propagates in the -direction with propagation constant . For a TM polarized surface wave, . The electric field in the upper half-space has the following form: (1) In the lower half-space, the electric field has a similar form as follows: (2) Fig. 2. Surface wave bound to a dielectric interface, decaying exponentially away from the surface. For the waves described above, Maxwell’s equations can be solved to obtain the following results [7]: (3) (4) (5) If is positive, then and are imaginary, and the waves do not decay with distance from the surface; they are simply plane waves propagating through the dielectric interface. Thus, TM surface waves do not exist on nonconductive dielectric materials. On the other hand, if is less than 1, or if it is imaginary, the solution describes a wave that is bound to the surface. These TM surface waves can occur on metals, or other materials with nonpositive dielectric constants. The solution for TE surface waves can also be obtained from the foregoing analysis by the principle of duality [1]. If the electric and magnetic fields are exchanged, and is substituted for , the solution above can be applied to the TE case. B. Metal Surfaces The effective, relative dielectric constant of a metal can be expressed in the following form [7]: (6) is the conductivity, which is given by the following equation: (7) is the mean electron collision time, is the electron charge, and and are the effective mass and the density, respectively, of the conduction electrons. For frequencies much lower than , including the mi￾crowave spectrum, the conductivity is primarily real, and much greater than unity, thus, the dielectric constant is a large imaginary number. Inserting (6) into (3) leads to a simple dispersion relation for surface waves at radio frequencies as follows: (8) Thus, surface waves propagate at nearly the speed of light in vacuum, and they travel for many wavelengths along the metal surface with little attenuation. By inserting (6) into (4), we can

SIEVENPIPER et al. : HIGH-IMPEDANCE ELECTROMAGNETIC SURFACES find the following expression for a, the decay constant of the in which the surface impedance is given by the following fields into the surrounding space: expression Zs(TM)=2c Conversely, TE waves can occur on a capacitive surface, with For good conductors at microwave frequencies, the urface the following impe ance waves extend a great distance into the surrounding space For example, on a copper surface, the electromagnetic fields Zs(TE)==oke (15) associated with a 10-GHz surface wave extend about 70m 2300 wavelengths into free space. Hence, at microwave The surface impedance of the textured metal surface described frequencies they are often described simply as surface currents, in this paper is characterized by an equivalent parallel resonant rather than surface waves. These surface currents are nothing LC circuit. At low frequencies it is inductive, and supports more than the normal alternating currents that can occur on TM waves. At high frequencies it is capacitive, and supports any conductor TE waves. Near the LC resonance frequency, the surface We can also determine ?, the surface-wave penetration impedance is very high. In this region, waves are not bound to depth into the metal. By inserting(6)into(5), we obtain the the surface; instead, they radiate readily into the surrounding following T≈(1+j) 00_(1+) (10) IIL. TEXTURED SURFACE Ght The concept of suppressing surface waves on metals is not Thus, we have derived the skin depth d from the surface-wave new. It has been done before using several geometries, such penetration depth [2]. The surface currents penetrate only a as a metal sheet covered with small bumps [81, [9], or a very small distance into the metal. For example, at 10 GHz, corrugated metal slab [11H-[19]. The novelty of this study the skin depth of copper is less than 1 um is the application of an array of lumped-circuit elements to From the skin depth, we can derive the surface impedance produce a thin two-dimensional structure that must generally of a fiat metal sheet [3].Using(10), we can express the current be described by band structure concepts, even though the in terms of the skin depth, assuming Eo is the electric field thickness and preiodicity are both much smaller than the at the surface operating wavelength. J(x)=aE2(x)=0Ec-m(1+)/ (ID)A. Bumpy Surfaces The magnetic field at the surface is found by integrating along Surface waves can be eliminated from a metal surface over a path surrounding the thin surface layer of current, extending a finite frequency band by applying a periodic texture, such far into the metal beyond the skin depth as follows as a lattice of small bumps. As surface waves scatter from the rows of bumps, the resulting interference prevents them J(r)da (12) from propagating, producing a two-dimensional electromag- netic bandgap. Such a structure has been studied at optical frequencies by Barnes et al.[8] and Kitson et al.[9] using a Thus, the surface impedance of a flat sheet of metal is derived triangular lattice of bumps, patterned on a silver film as follows When the wavelength is much longer than the period of two- dimensional lattice, the surface waves barely notice the small (13)bumps. At shorter wavelengths. the surface waves feel the ffects of the surface texture. When one-half wavelength fits The surface impedance has equal positive real and positive between the rows of bumps, this corresponds to the Brillouin imaginary parts, so the small surface resistance is accompanied zone boundary [10] of the two-dimensional lattice. At this by an equal amount of surface inductance. For example, the wavelength, a standing wave on the surface can have two surface impedance of copper at 10 GHz is 0.03(1+j) possible positions: with the wave crests centered on the bumps or with the nulls centered on the bumps, as shown in Fig 3 C. High-Impedance Surfaces These two modes have slightly different frequencies, separated By applying a texture to the metal surface, we can alter its by a small bandgap, within which surface waves cannot surface impedance, and thereby change its surface-wave prop- an extension of this"bumpy surface" in which the bandgap erties. The behavior of surface waves on a general impedance urface is derived in several electromagnetics textbooks [2] has been lowered in frequency by capacitive loading 3]. The derivation proceeds by assuming a wave that decays exponentially away from a boundary, with decay constant a. B. Corrugated Surfaces The boundary is characterized by its surface impedance. It The high-impedance surface can also be understood by can be shown that TM waves occur on an inductive surface. examining a similar structure. the corrugated surface. which

SIEVENPIPER et al.: HIGH-IMPEDANCE ELECTROMAGNETIC SURFACES 2061 find the following expression for , the decay constant of the fields into the surrounding space: (9) For good conductors at microwave frequencies, the surface waves extend a great distance into the surrounding space. For example, on a copper surface, the electromagnetic fields associated with a 10-GHz surface wave extend about 70 m, or 2300 wavelengths into free space. Hence, at microwave frequencies they are often described simply as surface currents, rather than surface waves. These surface currents are nothing more than the normal alternating currents that can occur on any conductor. We can also determine , the surface-wave penetration depth into the metal. By inserting (6) into (5), we obtain the following: (10) Thus, we have derived the skin depth from the surface-wave penetration depth [2]. The surface currents penetrate only a very small distance into the metal. For example, at 10 GHz, the skin depth of copper is less than 1 m. From the skin depth, we can derive the surface impedance of a flat metal sheet [3]. Using (10), we can express the current in terms of the skin depth, assuming is the electric field at the surface (11) The magnetic field at the surface is found by integrating along a path surrounding the thin surface layer of current, extending far into the metal beyond the skin depth as follows: (12) Thus, the surface impedance of a flat sheet of metal is derived as follows: (13) The surface impedance has equal positive real and positive imaginary parts, so the small surface resistance is accompanied by an equal amount of surface inductance. For example, the surface impedance of copper at 10 GHz is . C. High-Impedance Surfaces By applying a texture to the metal surface, we can alter its surface impedance, and thereby change its surface-wave prop￾erties. The behavior of surface waves on a general impedance surface is derived in several electromagnetics textbooks [2], [3]. The derivation proceeds by assuming a wave that decays exponentially away from a boundary, with decay constant . The boundary is characterized by its surface impedance. It can be shown that TM waves occur on an inductive surface, in which the surface impedance is given by the following expression: (14) Conversely, TE waves can occur on a capacitive surface, with the following impedance: (15) The surface impedance of the textured metal surface described in this paper is characterized by an equivalent parallel resonant circuit. At low frequencies it is inductive, and supports TM waves. At high frequencies it is capacitive, and supports TE waves. Near the resonance frequency, the surface impedance is very high. In this region, waves are not bound to the surface; instead, they radiate readily into the surrounding space. III. TEXTURED SURFACES The concept of suppressing surface waves on metals is not new. It has been done before using several geometries, such as a metal sheet covered with small bumps [8], [9], or a corrugated metal slab [11]–[19]. The novelty of this study is the application of an array of lumped-circuit elements to produce a thin two-dimensional structure that must generally be described by band structure concepts, even though the thickness and preiodicity are both much smaller than the operating wavelength. A. Bumpy Surfaces Surface waves can be eliminated from a metal surface over a finite frequency band by applying a periodic texture, such as a lattice of small bumps. As surface waves scatter from the rows of bumps, the resulting interference prevents them from propagating, producing a two-dimensional electromag￾netic bandgap. Such a structure has been studied at optical frequencies by Barnes et al. [8] and Kitson et al. [9] using a triangular lattice of bumps, patterned on a silver film. When the wavelength is much longer than the period of two￾dimensional lattice, the surface waves barely notice the small bumps. At shorter wavelengths, the surface waves feel the effects of the surface texture. When one-half wavelength fits between the rows of bumps, this corresponds to the Brillouin zone boundary [10] of the two-dimensional lattice. At this wavelength, a standing wave on the surface can have two possible positions: with the wave crests centered on the bumps, or with the nulls centered on the bumps, as shown in Fig. 3. These two modes have slightly different frequencies, separated by a small bandgap, within which surface waves cannot propagate. Our high-impedance surface can be considered as an extension of this “bumpy surface,” in which the bandgap has been lowered in frequency by capacitive loading. B. Corrugated Surfaces The high-impedance surface can also be understood by examining a similar structure, the corrugated surface, which

2062 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL, 47, NO Il, NOVEMBER 1999 Fig. 5. Origin of the capacitance and inductance in the high-impedance surfac netal sheet has a narrow surface-wave bandgap (a of the bandgap, in which the electric field wraps Layer 2 field extends across the bumps 6. ency for a given thickness by using capacitive loading, but it also suffers a reduction in bandwidth high impedance over a predetermined frequency band. Peri- odic two- or three-dimensional dielectric [2024], metallic [251[28], or metallodielectric [29H-33] structures that prevent 入 the propagation of electromagnetic waves are known as pho. tonic crystals [34-36 The high-impedance surface can be considered as a kind of two-dimensional photonic crystal that prevents the propagation of radio-frequency surface currents Fig. 4. Corrugated metal slab has high impedance at the top surface if the within the bandgap corrugations are one quarter-wavelength deer As the structure illustrated in Fig. 5 interacts with electro- magnetic waves, currents are induced in the top metal plates [1][12]. Numerous authors have also contributed general to build up on the ends of the plates, which can be described treatments of corrugated surfaces [13H-[15], and specific stud- as a capacitance. As the charges slosh back and forth, they ies of important structures [161-[19]. A corrugated surface flow around a long path through the vias and bottom plate a metal slab, into which a series of vertical slots have been an inductance Associated with these currents is a magnetic field and. thu cut, as depicted in Fig. 4. The slots are narrow, so that many We assign to the surface a sheet impedance equal to the of them fit within one wavelength across the slab. Each slot impedance of a parallel resonant circuit, consisting of the sheet can be regarded as a parallel-plate transmission line, running capacitance and the sheet inductance lown into the slab. and shorted at the bottom. If the slots are one quarter-wavelength deep, then the short circuit at the 2 bottom end is transformed by the length of the slots into an 1-∞2LC open-circuit at the top end. Thus, the impedance at the top The surface is inductive at low frequencies, and capacitive surface is very high at high frequencies. The impedance is very high near the If there are many slots per wavelength, the structure can resonance frequency wb be assigned an effective surface impedance equal to the impedance of the slots. The behavior of the corrugations is reduced to a single parameter-the boundary condition at the top surface. If the depth of the slots is greater than one We associate the high impedance with a forbidden frequency quarter-wavelength, the surface impedance is capacitive, and bandgap. In the two-layer geometry shown in Fig. 1,the TM surface waves are forbidden. Furthermore, a plane wave capacitors are formed by the fringing electric fields between polarized with the electric field perpendicular to the ridges adjacent metal patches, and the inductance is fixed by the will appear to be reflected with no phase reversal since the thickness of the structure. A three-layer design shown in Fig. 6 effective reflection plane is actually at the bottom of the slots, achieves a lower resonance frequency for a given thickness one quarter-wavelength away by using capacitive loading. In this geometry, parallel-plate formed by the top two C. High-Impedance Surfaces The high-impedance surface described here is an abstraction IV EFFECTIVE SURFACE IMPEDANCE MODEL of the corrugated surface, in which the corrugations have been Some of the properties of the high-impedance surface can folded up into lumped-circuit elements, and distributed in a be explained using an effective surface impedance model two-dimensional lattice. The surface impedance is modeled The surface is assigned an impedance equal to that of a as a parallel resonant circuit, which can be tuned to exhibit parallel resonant LC circuit, derived by geometry. The use

2062 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 47, NO. 11, NOVEMBER 1999 (a) (b) Fig. 3. Bumpy metal sheet has a narrow surface-wave bandgap. (a) Mode at the upper edge of the bandgap, in which the electric field wraps around the bumps. (b) Mode at the lower edge of the bandgap, in which the electric field extends across the bumps. Fig. 4. Corrugated metal slab has high impedance at the top surface if the corrugations are one quarter-wavelength deep. is discussed in various textbooks [2], [3], and review articles [11], [12]. Numerous authors have also contributed general treatments of corrugated surfaces [13]–[15], and specific stud￾ies of important structures [16]–[19]. A corrugated surface is a metal slab, into which a series of vertical slots have been cut, as depicted in Fig. 4. The slots are narrow, so that many of them fit within one wavelength across the slab. Each slot can be regarded as a parallel-plate transmission line, running down into the slab, and shorted at the bottom. If the slots are one quarter-wavelength deep, then the short circuit at the bottom end is transformed by the length of the slots into an open-circuit at the top end. Thus, the impedance at the top surface is very high. If there are many slots per wavelength, the structure can be assigned an effective surface impedance equal to the impedance of the slots. The behavior of the corrugations is reduced to a single parameter—the boundary condition at the top surface. If the depth of the slots is greater than one quarter-wavelength, the surface impedance is capacitive, and TM surface waves are forbidden. Furthermore, a plane wave polarized with the electric field perpendicular to the ridges will appear to be reflected with no phase reversal since the effective reflection plane is actually at the bottom of the slots, one quarter-wavelength away. C. High-Impedance Surfaces The high-impedance surface described here is an abstraction of the corrugated surface, in which the corrugations have been folded up into lumped-circuit elements, and distributed in a two-dimensional lattice. The surface impedance is modeled as a parallel resonant circuit, which can be tuned to exhibit Fig. 5. Origin of the capacitance and inductance in the high-impedance surface. Fig. 6. Three-layer high-impedance surface achieves a lower operating fre￾quency for a given thickness by using capacitive loading, but it also suffers a reduction in bandwidth. high impedance over a predetermined frequency band. Peri￾odic two- or three-dimensional dielectric [20]–[24], metallic [25]–[28], or metallodielectric [29]–[33] structures that prevent the propagation of electromagnetic waves are known as pho￾tonic crystals [34]–[36]. The high-impedance surface can be considered as a kind of two-dimensional photonic crystal that prevents the propagation of radio-frequency surface currents within the bandgap. As the structure illustrated in Fig. 5 interacts with electro￾magnetic waves, currents are induced in the top metal plates. A voltage applied parallel to the top surface causes charges to build up on the ends of the plates, which can be described as a capacitance. As the charges slosh back and forth, they flow around a long path through the vias and bottom plate. Associated with these currents is a magnetic field and, thus, an inductance. We assign to the surface a sheet impedance equal to the impedance of a parallel resonant circuit, consisting of the sheet capacitance and the sheet inductance (16) The surface is inductive at low frequencies, and capacitive at high frequencies. The impedance is very high near the resonance frequency (17) We associate the high impedance with a forbidden frequency bandgap. In the two-layer geometry shown in Fig. 1, the capacitors are formed by the fringing electric fields between adjacent metal patches, and the inductance is fixed by the thickness of the structure. A three-layer design shown in Fig. 6 achieves a lower resonance frequency for a given thickness by using capacitive loading. In this geometry, parallel-plate capacitors are formed by the top two overlapping layers. IV. EFFECTIVE SURFACE IMPEDANCE MODEL Some of the properties of the high-impedance surface can be explained using an effective surface impedance model. The surface is assigned an impedance equal to that of a parallel resonant circuit, derived by geometry. The use

SIEVENPIPER et al. : HIGH-IMPEDANCE ELECTROMAGNETIC SURFACES 2063 Below resonance, TM surface waves are supported. At low frequencies, they lie very near the light line, and the fields 25 extend many wavelengths beyond the surface, as they do a flat metal surface. Near the resonant frequency, the surface waves are tightly bound to the sheet, and have a very low roup velocity, as seen by the fact that the dispersion curve esonance frequency is bent over, away from the light line. In the effective surface impedance limit, there is no Brillouin zone boundary, and the TM dispersion curve approaches the resonance frequency asymptotically. Thus, this approximation fails to predict the Above the resonance frequency, the surface is capacitive, and TE waves are supported. The lower end of the dispersion curve is close to the light line, and the waves are weakly bound to the surface, extending far into the surrounding space. As the Wave Vector [1/cm] frequency is increased, the curve bends away from the light Fig. 7. Dispersion diagram of the high-impedance surface, calculated using line, and the waves are more tightly bound to the surface the effective surface impedance The slope of the dispersion curve indicates that the waves feel an effective index of refraction that is greater than unity This is because a significant portion of the electric field is of lumped parameters to describe electromagnetic structures concentrated in the capacitors. The effective dielectric constant is valid as long as the wavelength is much longer than the size of the individual features. This short wave vector range of a material is enhanced if it is permeated with capacitor-like is also the regime of effective medium theory. The effective structures The te waves that lie to the left of the light line exist as surface impedance model can predict the reflection properties leaky waves that are damped by radiation. Radiation occurs from surfaces with a real impedance, thus, the leaky modes to the bandgap itself, which by definition must extend to large the left-hand side of the light line occur at the resonance fre- wave vector quency. The radiation from these leaky tE modes is modeled as a resistor in parallel with the high-impedance surface, which A. Surface Waves blurs the resonance frequency. Thus, the leaky waves actually We can determine the dispersion relation for surface waves radiate within a finite bandwidth, as shown in Fig.7.The in the context of the effective surface impedance model by damping resistance is the impedance of free space, projected inserting(1)into Maxwells equations. The wave vector k is onto the surface according to the angle of radiation. Small related to the spatial decay constant a and the frequency, w wave vectors represent radiation perpendicular to the surface by the following expression: while wave vectors near the light line represent radiation at k2=pe02+a2 grazing angles. For a tE polarized plane wave, the magnetic (18) field, H, projected on the surface at angle 0 with respect to For TM waves we can combine(18)with(14)to find the normal is H(0)=Hoods(0), while the electric field is just E(0= Eo. The impedance of free space, as seen by the a function of w, n=VHo/Eo is the impedance of free space and c=1/V/HOE0 expression surface for radiation at an angle, is given by the following is the speed of light in vacuum 2x(O)=B(6 1) (19) Thus. the radiation resistance is 377 3 for small wave We can find a similar expression for TE waves by combining vectors and normal radiation, but the damping resistance (18) with(15)as follows approaches infinity for wave vectors near the light line. Infinite resistance in a parallel resonant circuit corresponds to no damping, so the radiative band is reduced to zero width ATE= (20) for grazing angles near the light line. The high-impedance radiative region is shown as a shaded area, representing the By inserting(16)into(19)and(20), we can plot the disper- blurring of the leaky waves by radiation damping. In place of sion diagram for surface waves. in the context of the effective a bandgap, the effective surface impedance model predicts a surface impedance model. Depending on geometry, typical frequency band characterized by radiation damping values for the shee and sheet ing 0 layer structure are about 0.05 pF2, and 2 nH2, respectively. The B. Reflection Phase complete dispersion diagram, calculated using the effective The surface impedance determines the boundary condition medium model, is shown in Fig. 7 at the surface for the standing wave formed by incident and

SIEVENPIPER et al.: HIGH-IMPEDANCE ELECTROMAGNETIC SURFACES 2063 Fig. 7. Dispersion diagram of the high-impedance surface, calculated using the effective surface impedance model. of lumped parameters to describe electromagnetic structures is valid as long as the wavelength is much longer than the size of the individual features. This short wave vector range is also the regime of effective medium theory. The effective surface impedance model can predict the reflection properties and some features of the surface-wave band structure, but not the bandgap itself, which by definition must extend to large wave vectors. A. Surface Waves We can determine the dispersion relation for surface waves in the context of the effective surface impedance model by inserting (1) into Maxwell’s equations. The wave vector is related to the spatial decay constant and the frequency, by the following expression: (18) For TM waves we can combine (18) with (14) to find the following expression for as a function of , in which is the impedance of free space and is the speed of light in vacuum: (19) We can find a similar expression for TE waves by combining (18) with (15) as follows: (20) By inserting (16) into (19) and (20), we can plot the disper￾sion diagram for surface waves, in the context of the effective surface impedance model. Depending on geometry, typical values for the sheet capacitance and sheet inductance of a two￾layer structure are about 0.05 pF , and 2 nH , respectively. The complete dispersion diagram, calculated using the effective medium model, is shown in Fig. 7. Below resonance, TM surface waves are supported. At low frequencies, they lie very near the light line, and the fields extend many wavelengths beyond the surface, as they do on a flat metal surface. Near the resonant frequency, the surface waves are tightly bound to the sheet, and have a very low group velocity, as seen by the fact that the dispersion curve is bent over, away from the light line. In the effective surface impedance limit, there is no Brillouin zone boundary, and the TM dispersion curve approaches the resonance frequency asymptotically. Thus, this approximation fails to predict the bandgap. Above the resonance frequency, the surface is capacitive, and TE waves are supported. The lower end of the dispersion curve is close to the light line, and the waves are weakly bound to the surface, extending far into the surrounding space. As the frequency is increased, the curve bends away from the light line, and the waves are more tightly bound to the surface. The slope of the dispersion curve indicates that the waves feel an effective index of refraction that is greater than unity. This is because a significant portion of the electric field is concentrated in the capacitors. The effective dielectric constant of a material is enhanced if it is permeated with capacitor-like structures. The TE waves that lie to the left of the light line exist as leaky waves that are damped by radiation. Radiation occurs from surfaces with a real impedance, thus, the leaky modes to the left-hand side of the light line occur at the resonance fre￾quency. The radiation from these leaky TE modes is modeled as a resistor in parallel with the high-impedance surface, which blurs the resonance frequency. Thus, the leaky waves actually radiate within a finite bandwidth, as shown in Fig. 7. The damping resistance is the impedance of free space, projected onto the surface according to the angle of radiation. Small wave vectors represent radiation perpendicular to the surface, while wave vectors near the light line represent radiation at grazing angles. For a TE polarized plane wave, the magnetic field, , projected on the surface at angle with respect to normal is , while the electric field is just . The impedance of free space, as seen by the surface for radiation at an angle, is given by the following expression: (21) Thus, the radiation resistance is 377 for small wave vectors and normal radiation, but the damping resistance approaches infinity for wave vectors near the light line. Infinite resistance in a parallel resonant circuit corresponds to no damping, so the radiative band is reduced to zero width for grazing angles near the light line. The high-impedance radiative region is shown as a shaded area, representing the blurring of the leaky waves by radiation damping. In place of a bandgap, the effective surface impedance model predicts a frequency band characterized by radiation damping. B. Reflection Phase The surface impedance determines the boundary condition at the surface for the standing wave formed by incident and

2064 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL, 47, NO Il, NOVEMBER 1999 Although the surface exhibits high impedance, it is not actually devoid of current. (If there were no current, electro- magnetic waves would be transmitted right through the ground plane. )However, the resonant structure provides a phase shift, thus. the image currents in the surface reinforce the currents in the antenna, instead of canceling them To the left-hand side of the light line in Fig. 7, we can determine the frequency range over which the radiation effi- ciency is high by using a circuit model, in which the antenna is modeled as a current source. The textured surface is modeled as an LC circuit in parallel with the antenna, and the radiation into free space is modeled as a resistor with a value of po/Eo/cos(0)= 377 S/cos(0). The amount of power dissipated in the resistor is a measure of the radiation efficiency of the antenna The maximum power dissipated in istor occurs at Fig 8. Reflection phase of the high-impedance surtace, calculated using the the LC resonance frequency of the ffective surface the surface reactance crosses through frequencies, or at very high frequencies, the current is shunted reflected waves. If the surface has low impedance, such as through the inductor or the capacitor, and the power flowing in the case of a good conductor, the ratio of electric field to to the resistor is reduced. It can be shown that the frequencies magnetic field is small. The electric field has a node at the where the radiation drops to half of its maximum value occur surface, and the magnetic field has an antinode. Conversely, when the magnitude of the surface impedance is equal to the for a high impedance surface, the electric field has an antinode impedance of free space. For normal radiation, we have the at the surface, while the magnetic field has a node. Another following equation term for such a surface is an artificial "magnetic conductor Recent work involving grounded frequency selective surfaces has also been shown to mimic a magnetic conductor [37] 2LC=7 However, these structures do not possess a complete surface- This can be solved for w to yield the following equation wave bandgap, since they lack the vertical conducting vias, which interact with the vertical electric field of tm surface (23) waves Typical parameters for a two-layer ground plane are 2 nH2 For typical geometries, L is usually on the order of I nH, of inductance, and 0.05 pF2 of capacitance. For these values, and C is in the range of 0.05-10 pF. With these values, the the reflection phase is plotted in Fig 8. At very low frequen- terms involving 1/rC are much smaller than the 1/LC cies, the reflection phase is T, and the structure behaves like terms, so we will eliminate them. This approximation yields an ordinary flat metal surface. The reflection phase slopes the following expression for the edges of the operating band downward, and eventually crosses through zero at the reso- nance frequency. Above the resonance frequency, the phase u=Wb11士 to -T. The phase falls within T/2 and -T/2 when the ude of the surface impedance exceeds the impedance The resonance frequency is wb=1/VLC, and Zo=VL/C rather than out-of-phase, and antenna elements may lie directly is the characteristic impedance of the LC circuit. With the adjacent to the surface without being shorted out parameters for L, C, and n given above, Zo is usually significantly smaller than n. Thus, the square root can be expanded in the following approximation (1±1z An antenna lying parallel to the textured surface will see the impedance of free space on one side, and the impedance The two frequencies designated by the t signs delimit the of the ground plane on the other side. Where the textured range over which an antenna would radiate efficiently or surface has low impedance, far from the resonance frequency, such a surface. The total bandwidth is roughly equal to the antenna current is mirrored by an opposing current in the characteristic impedance of the surface divided by the the surface. Since the antenna is shorted out by the nearby impedance of free space conductor, the radiation efficiency is very low. Within the forbidden bandgap near resonance, the textured surface has much higher impedance than free space, so the antenna is not shorted out. In this range of frequencies, the radiation This is also the bandwidth over which the reflection coefficient ency is high falls between +r/2 and -T/2, and image currents are more

2064 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 47, NO. 11, NOVEMBER 1999 Fig. 8. Reflection phase of the high-impedance surface, calculated using the effective surface impedance model. reflected waves. If the surface has low impedance, such as in the case of a good conductor, the ratio of electric field to magnetic field is small. The electric field has a node at the surface, and the magnetic field has an antinode. Conversely, for a high impedance surface, the electric field has an antinode at the surface, while the magnetic field has a node. Another term for such a surface is an artificial “magnetic conductor.” Recent work involving grounded frequency selective surfaces has also been shown to mimic a magnetic conductor [37]. However, these structures do not possess a complete surface￾wave bandgap, since they lack the vertical conducting vias, which interact with the vertical electric field of TM surface waves. Typical parameters for a two-layer ground plane are 2 nH of inductance, and 0.05 pF of capacitance. For these values, the reflection phase is plotted in Fig. 8. At very low frequen￾cies, the reflection phase is , and the structure behaves like an ordinary flat metal surface. The reflection phase slopes downward, and eventually crosses through zero at the reso￾nance frequency. Above the resonance frequency, the phase returns to . The phase falls within and when the magnitude of the surface impedance exceeds the impedance of free space. Within this range, image currents are in-phase, rather than out-of-phase, and antenna elements may lie directly adjacent to the surface without being shorted out. C. Radiation Bandwidth An antenna lying parallel to the textured surface will see the impedance of free space on one side, and the impedance of the ground plane on the other side. Where the textured surface has low impedance, far from the resonance frequency, the antenna current is mirrored by an opposing current in the surface. Since the antenna is shorted out by the nearby conductor, the radiation efficiency is very low. Within the forbidden bandgap near resonance, the textured surface has much higher impedance than free space, so the antenna is not shorted out. In this range of frequencies, the radiation efficiency is high. Although the surface exhibits high impedance, it is not actually devoid of current. (If there were no current, electro￾magnetic waves would be transmitted right through the ground plane.) However, the resonant structure provides a phase shift, thus, the image currents in the surface reinforce the currents in the antenna, instead of canceling them. To the left-hand side of the light line in Fig. 7, we can determine the frequency range over which the radiation effi- ciency is high by using a circuit model, in which the antenna is modeled as a current source. The textured surface is modeled as an circuit in parallel with the antenna, and the radiation into free space is modeled as a resistor with a value of . The amount of power dissipated in the resistor is a measure of the radiation efficiency of the antenna. The maximum power dissipated in the resistor occurs at the resonance frequency of the ground plane, where the surface reactance crosses through infinity. At very low frequencies, or at very high frequencies, the current is shunted through the inductor or the capacitor, and the power flowing to the resistor is reduced. It can be shown that the frequencies where the radiation drops to half of its maximum value occur when the magnitude of the surface impedance is equal to the impedance of free space. For normal radiation, we have the following equation: (22) This can be solved for to yield the following equation: (23) For typical geometries, is usually on the order of 1 nH, and is in the range of 0.05–10 pF. With these values, the terms involving are much smaller than the terms, so we will eliminate them. This approximation yields the following expression for the edges of the operating band: (24) The resonance frequency is , and is the characteristic impedance of the circuit. With the parameters for , and given above, is usually significantly smaller than . Thus, the square root can be expanded in the following approximation: (25) The two frequencies designated by the signs delimit the range over which an antenna would radiate efficiently on such a surface. The total bandwidth is roughly equal to the characteristic impedance of the surface divided by the impedance of free space (26) This is also the bandwidth over which the reflection coefficient falls between and , and image currents are more

SIEVENPIPER et al. : HIGH-IMPEDANCE ELECTROMAGNETIC SURFACES 2065 M Fig 9. Square geometry studied using the finite-element model Fig. 10. Surface nd structure of the high-impedance surface, model. The radiation broadening of the te hase than out-of-phase. It represents the maximum usable above the light Ii error width of a flush-mounted antenna on a resonant surface of this type The relative bandwidth Aw/w is proportional to VL/C thus, if the capacitance is increased, the bandwidth suffers Surface Since the thickness is related to the inductance. the more the Under esonance frequency is reduced for a given thickness, the more the bandwidth is diminished Microwave Absorber V. FINITE-ELEMENT MODEL In the effective surface impedance model described above Coax he properties of the surface are summarized into a single Probe parameter, namely the surface impedance. Such a model cor- rectly predicts the reflection properties of the high-impedance surface and some features of the surface-wave bands. how- ver, it does not predict an actual bandgap. Neverthele we have found experimentally that the surface-wave bandgap edges occur where the reflection phase is equal to +T/2, thus this generally corresponds to the width of the surface-wave bandgap. Within this region, surface currents radiate It is necessary to obtain more accurate results using a finite- (a)TM surface-wave measurement using vertical monopole probe element model, in which the detailed geometry of the surface he probes couple to the vertical electric field of TM surface waves. nt using horizontal monopole probe antennas. texture is included explicitly. In the finite-element model, the couple to the horizontal electric field of TE surface waves metal and dielectric regions of one unit cell are discretized on a grid. The electric field at all points on the grid can be reduced to an eigenvalue equation, which may be solved numerically the graph by a dotted line. These qualitatively Bloch boundary conditions are used, in which the fields at with the effective medium model. The finite-element method one edge of the cell are related to the fields at the opposite also predicts higher frequency bands that are seen in the frequencies for a particular wave vector, and the procedure mode ements, but do not appear in the effective medium edge by the wave vector. The calculation yields the allowed is repeated for each wave vector to produce the dispersion According to the finite-element model, the TM band does diagram. The structure analyzed by the finite-element method not reach the TE band edge, but stops below it, forming a was a two-layer high-impedance surface with square geometry, bandgap. The Te band slopes upward upon crossing the light shown in Fig 9. The lattice constant was 2.4 mm, the spacing line. Thus, the finite-element model predicts a surface-wave between the plates was 0.15 mm, and the width of the vias bandgap that spans from the edge of the TM band,to was 0.36 mm. The volume below the square plates was filled point where the TE band crosses the light line. The resonance with e=2.2. and the total thickness was 1.6 mm frequency is centered in the forbidden bandgap The results of the finite-element calculation are shown in In both the TM and tE bands, the k=0 state represents 10. The TM band follows the light line up to a certain a continuous sheet of current. The lowest TM mode, at zero frequency, where it suddenly becomes very flat. The TE band frequency, is simply a sheet of constant current-a dc mode begins at a higher frequency, and continues upward with a The highest TM mode, at the brillouin zone edge, is a standing slope of less than the vacuum speed of light, which is indicated wave in which each row of metal protrusions has opposite

SIEVENPIPER et al.: HIGH-IMPEDANCE ELECTROMAGNETIC SURFACES 2065 Fig. 9. Square geometry studied using the finite-element model. in-phase than out-of-phase. It represents the maximum usable bandwidth of a flush-mounted antenna on a resonant surface of this type. The relative bandwidth is proportional to , thus, if the capacitance is increased, the bandwidth suffers. Since the thickness is related to the inductance, the more the resonance frequency is reduced for a given thickness, the more the bandwidth is diminished. V. FINITE-ELEMENT MODEL In the effective surface impedance model described above, the properties of the surface are summarized into a single parameter, namely the surface impedance. Such a model cor￾rectly predicts the reflection properties of the high-impedance surface, and some features of the surface-wave bands. How￾ever, it does not predict an actual bandgap. Nevertheless, we have found experimentally that the surface-wave bandgap edges occur where the reflection phase is equal to , thus, this generally corresponds to the width of the surface-wave bandgap. Within this region, surface currents radiate. It is necessary to obtain more accurate results using a finite￾element model, in which the detailed geometry of the surface texture is included explicitly. In the finite-element model, the metal and dielectric regions of one unit cell are discretized on a grid. The electric field at all points on the grid can be reduced to an eigenvalue equation, which may be solved numerically. Bloch boundary conditions are used, in which the fields at one edge of the cell are related to the fields at the opposite edge by the wave vector. The calculation yields the allowed frequencies for a particular wave vector, and the procedure is repeated for each wave vector to produce the dispersion diagram. The structure analyzed by the finite-element method was a two-layer high-impedance surface with square geometry, shown in Fig. 9. The lattice constant was 2.4 mm, the spacing between the plates was 0.15 mm, and the width of the vias was 0.36 mm. The volume below the square plates was filled with , and the total thickness was 1.6 mm. The results of the finite-element calculation are shown in Fig. 10. The TM band follows the light line up to a certain frequency, where it suddenly becomes very flat. The TE band begins at a higher frequency, and continues upward with a slope of less than the vacuum speed of light, which is indicated Fig. 10. Surface-wave band structure of the high-impedance surface, calcu￾lated using a finite-element model. The radiation broadening of the TE modes above the light line is indicated by error bars. (a) (b) Fig. 11. (a) TM surface-wave measurement using vertical monopole probe antennas. The probes couple to the vertical electric field of TM surface waves. (b) TE surface-wave measurement using horizontal monopole probe antennas. The probes couple to the horizontal electric field of TE surface waves. on the graph by a dotted line. These results agree qualitatively with the effective medium model. The finite-element method also predicts higher frequency bands that are seen in the measurements, but do not appear in the effective medium model. According to the finite-element model, the TM band does not reach the TE band edge, but stops below it, forming a bandgap. The TE band slopes upward upon crossing the light line. Thus, the finite-element model predicts a surface-wave bandgap that spans from the edge of the TM band, to the point where the TE band crosses the light line. The resonance frequency is centered in the forbidden bandgap. In both the TM and TE bands, the state represents a continuous sheet of current. The lowest TM mode, at zero frequency, is simply a sheet of constant current—a dc mode. The highest TM mode, at the Brillouin zone edge, is a standing wave in which each row of metal protrusions has opposite

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL, 47, NO Il, NOVEMBER 1999 (b) 5 Frequency [ GHz ave transmission across a flat metal surface.(b)TM surface-wave transmission across a two-layer high- impedanc ission across a two-layer high-impedance surface. The strong fluctuations are due to multipath inter (b)and (c) charge. The lowest TE mode is a sheet of current that is surface wave. Another method for coupling to surface waves, continuous in space, but oscillating at the lC resonance which is more practical at microwave frequencies, is to use frequency, at the origin of k-space. The te band slopes very small probe. A point source launches all wave vectors smoothly upward in frequency, crossing through the light line thus, a small antenna brought near the surface is capable of at some point. At the highest TE mode, at the Brillouin zone coupling to surface-wave modes. The antenna geometry can boundary, transverse currents flow in opposite directions on be tailored to distinguish surface-wave polarization each row of protrusions In TM surface waves, the electric field forms loops that ex- In the other upper bands, the electric field is primarily tend vertically out of the surface. TM waves can be measured concentrated in the region below the capacitor plates. The using a pair of small monopole antennas oriented normally modes in these bands resemble the modes in a parallel-plate with respect to the surface, as shown in Fig. 11(a). The vertical waveguide. The first of these modes occurs at about the electric field of the probe couples to the vertical electric field requency where one half-wavelength fits between the rows of the TM surface waves In TE surface waves, the electric of metal vias field is parallel to the surface. They can be measured with a pair of small monopole probes oriented parallel to the sheet, MEASURING SURFACE PROPERTIES as shown in Fig. 11(b). The horizontal electric field of the antenna couples to the horizontal electric field of the Te wave On a flat metal sheet, a TM surface-wave measurement pro- Since surface waves cannot generally couple to external duces the results shown in Fig. 12(a). The surface under test plane waves, specialized methods must be used to measure was a 12-cm- sheet of flat metal. The measurement represents them. At optical frequencies, surface plasmons are often the transmission between a pair of monopole probes oriented studied using a technique called prism coupling [8]. A prism is vertically at the edges of the metal sheet. (A TE surface- placed next to the surface, and the refractive index of the prism wave measurement produces no significant signal because any is used to match the wave vector of a probe beam to that of a antenna that excites te waves is shorted out on a conducting

2066 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 47, NO. 11, NOVEMBER 1999 (a) (b) (c) Fig. 12. (a) TM surface-wave transmission across a flat metal surface. (b) TM surface-wave transmission across a two-layer high-impedance surface. (c) TE surface-wave transmission across a two-layer high-impedance surface. The strong fluctuations are due to multipath interference. The forbidden bandgap is shown for cases (b) and (c). charge. The lowest TE mode is a sheet of current that is continuous in space, but oscillating at the resonance frequency, at the origin of -space. The TE band slopes smoothly upward in frequency, crossing through the light line at some point. At the highest TE mode, at the Brillouin zone boundary, transverse currents flow in opposite directions on each row of protrusions. In the other upper bands, the electric field is primarily concentrated in the region below the capacitor plates. The modes in these bands resemble the modes in a parallel-plate waveguide. The first of these modes occurs at about the frequency where one half-wavelength fits between the rows of metal vias. VI. MEASURING SURFACE PROPERTIES A. Surface Waves Since surface waves cannot generally couple to external plane waves, specialized methods must be used to measure them. At optical frequencies, surface plasmons are often studied using a technique called prism coupling [8]. A prism is placed next to the surface, and the refractive index of the prism is used to match the wave vector of a probe beam to that of a surface wave. Another method for coupling to surface waves, which is more practical at microwave frequencies, is to use a very small probe. A point source launches all wave vectors, thus, a small antenna brought near the surface is capable of coupling to surface-wave modes. The antenna geometry can be tailored to distinguish surface-wave polarization. In TM surface waves, the electric field forms loops that ex￾tend vertically out of the surface. TM waves can be measured using a pair of small monopole antennas oriented normally with respect to the surface, as shown in Fig. 11(a). The vertical electric field of the probe couples to the vertical electric field of the TM surface waves. In TE surface waves, the electric field is parallel to the surface. They can be measured with a pair of small monopole probes oriented parallel to the sheet, as shown in Fig. 11(b). The horizontal electric field of the antenna couples to the horizontal electric field of the TE waves. On a flat metal sheet, a TM surface-wave measurement pro￾duces the results shown in Fig. 12(a). The surface under test was a 12-cm sheet of flat metal. The measurement represents the transmission between a pair of monopole probes oriented vertically at the edges of the metal sheet. (A TE surface￾wave measurement produces no significant signal because any antenna that excites TE waves is shorted out on a conducting

SIEVENPIPER et al. : HIGH-IMPEDANCE ELECTROMAGNETIC SURFACES 2067 surface. It is only on the textured surface, with its unusual surface impedance, that significant TE transmission signal Transmits levels can be obtained. Horn The tM data has variations of 10-15 dB. but remains relatively flat over a broad spectrum. The variations are produced by multipath interference, or speckle, which occurs in coherent measurements whenever multiple signal paths are Horn Microwave Absorber present Multipath interference can be distinguished from other effects because it is characterized by narrow-band fading, Fig 13. Reflection phase measurement performed using a pair of hom whose details depend on the exact antenna position. The antennas. The anechoic chamber used in these experiments measured 30 cm transmission drops off at low frequencies because the small X 30 cm x 60 cm, and the hole for the sample measured 10 cm X 10 probes are inefficient at exciting long wavelengths A typical TM surface-wave measurement on a textured surface is shown in Fig. 12(b). The size of the sheet and the Out-of-Phase measurement technique were the same as those used for the flat metal surface. The structure consisted of a triangular array 2 2 A of hexagonal patches as shown in Fig. l, with a period of 2 2.54 mm and a gap between the patches of 0. 15 mm. The thickness of the board was 1.55 mm and the dielectric constant In-Phase was 2.2 The transmission is strong at low frequencies, and exhibits the same multipath interference seen on the metal surface. At I 1 GHz, the transmission drops by about 30 dB, indicating the Out-of-Phase edge of the TM surface-wave band. Beyond this frequency the transmission level remains low and fat, eventually sloping oward at much higher frequencies because of weak coupling Frequency [GHz to TE surface waves. The te band edge is not apparent in Fig 14. Measured reflection phase of a two-layer high-impedance surface this measurement, but the region corresponding to the surface- wave bandgap is indicated on the graph by an arrow A tE transmission measurement of the same textured sur- A reference measurement is taken of a surface with known face is shown in Fig. 12(c). It was taken using a pair of renection properties, such as a flat sheet of metal, and all subsequent measurements are divided by this reference. A transmission is weak at low frequencies, and strong at high factor of m is added to the phase data to account for the requencies, the reverse profile of the TM data. A sharp Jump a reflection phase of T of 30 dB occurs at 17 GHz, indicating the te band edge Beyond this frequency, the transmission is flat, with only small The reflection phase of the high impedance surface is shown in Fig. 14. At low frequencies, it reflects with a T phase to Tm surface waves. so there is an additional transmission shift just like a metal surface. As the frequency is increased, peak at 11 GHZ, at the tm band edge, where the density of the phase slopes downward, and eventually crosses through TM states is high. Both TM and TE probes tend to couple zero at the resonance frequency of the structure. At higher slightly to the opposite surface-wave polarizations. However, frequencies, the phase continues to slope downward, and the cross coupling is greater with the TE probe because it lacks and-T/2, indicated on the graph by arrows, plane waves are he symmetry of the vertical monopole A surface-wave bandgap is measured between the TM band reflected in-phase, rather than out-of-phase. This range also edge at 11 GHz and the TE band edge at 17 GHz. Within this corresponds to the measured surface-wave bandgap, indicated Currents cannot propagate across the surface, and any induced edges falling approximately at the points where the phase currents radiate from the surface crosses through丌/2and-丌/2, respectively C. Low-Frequency Structures B. Reflection Phase With two-layer construction, the capacitors are formed by The reflection phase of the high-impedance surface can be the fringing capacitance between two metal plates lying edge- measured using two microwave horn antennas, as shown in to-edge, usually separated by a few hundred microns. If the Fig. 13. The measurement is done in an anechoic chamber substrate has a dielectric constant between 2-10. and the lined with microwave absorbing foam. The two horns are period is a few millimeters, the capacitance is generally on placed next to each other, aimed at the surface. Two windows the order of a few tens of femtofarads. With a thickness of are cut in the chamber, one for the antennas, and one for the a few millimeters, the inductance is a few nanohenry, so the surface under test resonance frequency is on typically the order of about 10 gHz

SIEVENPIPER et al.: HIGH-IMPEDANCE ELECTROMAGNETIC SURFACES 2067 surface. It is only on the textured surface, with its unusual surface impedance, that significant TE transmission signal levels can be obtained.) The TM data has variations of 10–15 dB, but remains relatively flat over a broad spectrum. The variations are produced by multipath interference, or speckle, which occurs in coherent measurements whenever multiple signal paths are present. Multipath interference can be distinguished from other effects because it is characterized by narrow-band fading, whose details depend on the exact antenna position. The transmission drops off at low frequencies because the small probes are inefficient at exciting long wavelengths. A typical TM surface-wave measurement on a textured surface is shown in Fig. 12(b). The size of the sheet and the measurement technique were the same as those used for the flat metal surface. The structure consisted of a triangular array of hexagonal patches as shown in Fig. 1, with a period of 2.54 mm and a gap between the patches of 0.15 mm. The thickness of the board was 1.55 mm, and the dielectric constant was 2.2. The transmission is strong at low frequencies, and exhibits the same multipath interference seen on the metal surface. At 11 GHz, the transmission drops by about 30 dB, indicating the edge of the TM surface-wave band. Beyond this frequency, the transmission level remains low and flat, eventually sloping upward at much higher frequencies because of weak coupling to TE surface waves. The TE band edge is not apparent in this measurement, but the region corresponding to the surface￾wave bandgap is indicated on the graph by an arrow. A TE transmission measurement of the same textured sur￾face is shown in Fig. 12(c). It was taken using a pair of small coaxial probes, oriented parallel to the surface. The transmission is weak at low frequencies, and strong at high frequencies, the reverse profile of the TM data. A sharp jump of 30 dB occurs at 17 GHz, indicating the TE band edge. Beyond this frequency, the transmission is flat, with only small fluctuations due to speckle. The TE probes also couple slightly to TM surface waves, so there is an additional transmission peak at 11 GHZ, at the TM band edge, where the density of TM states is high. Both TM and TE probes tend to couple slightly to the opposite surface-wave polarizations. However, the cross coupling is greater with the TE probe because it lacks the symmetry of the vertical monopole. A surface-wave bandgap is measured between the TM band edge at 11 GHz and the TE band edge at 17 GHz. Within this range, neither polarization produces significant transmission. Currents cannot propagate across the surface, and any induced currents radiate from the surface. B. Reflection Phase The reflection phase of the high-impedance surface can be measured using two microwave horn antennas, as shown in Fig. 13. The measurement is done in an anechoic chamber lined with microwave absorbing foam. The two horns are placed next to each other, aimed at the surface. Two windows are cut in the chamber, one for the antennas, and one for the surface under test. Fig. 13. Reflection phase measurement performed using a pair of horn antennas. The anechoic chamber used in these experiments measured 30 cm 30 cm 60 cm, and the hole for the sample measured 10 cm 10 cm. Fig. 14. Measured reflection phase of a two-layer high-impedance surface. A reference measurement is taken of a surface with known reflection properties, such as a flat sheet of metal, and all subsequent measurements are divided by this reference. A factor of is added to the phase data to account for the reference scan of the metal sheet, which is known to have a reflection phase of . The reflection phase of the high impedance surface is shown in Fig. 14. At low frequencies, it reflects with a phase shift just like a metal surface. As the frequency is increased, the phase slopes downward, and eventually crosses through zero at the resonance frequency of the structure. At higher frequencies, the phase continues to slope downward, and eventually approaches . Within the region between and , indicated on the graph by arrows, plane waves are reflected in-phase, rather than out-of-phase. This range also corresponds to the measured surface-wave bandgap, indicated on the graph by a shaded region, with the TM and TE band edges falling approximately at the points where the phase crosses through and , respectively. C. Low-Frequency Structures With two-layer construction, the capacitors are formed by the fringing capacitance between two metal plates lying edge￾to-edge, usually separated by a few hundred microns. If the substrate has a dielectric constant between 2–10, and the period is a few millimeters, the capacitance is generally on the order of a few tens of femtofarads. With a thickness of a few millimeters, the inductance is a few nanohenrys, so the resonance frequency is on typically the order of about 10 GHz.

2068 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL, 47, NO Il, NOVEMBER 1999 -40 surface currents, which cause multipath interference and backward radiation (b)Surface waves are suppressed on a high-impedance ground plane low enough that the free-space wavelength is much greater han the probe length, which is only a few millimeters, so the annas tend to ually well to TM and te mo Transmission can be seen in both the tm and te bands. and a gap is visible between 2.2-2.5 GHz The reflection phase is shown in Fig. 15(b). The region corresponding to the surface-wave bandgap is shaded. Inside Fig. 15. (a) Surface-wave tran on across a three-layer high-impedance this gap, the reflection phase crosses through zero, and plane ing.(b)Reflection phase of a three-layer high-impedance surfae citive load. surface. The lower resonance frequency is achieved through capa waves are reflected in-phase rather than out-of-phase VIL ANtENNAS If the desired resonance frequency is less than about 5 GH the thickness can be kept within reasonable limits by using The high-impedance surface has proven useful as an antenna nree-layer construction, in which the capacitors are formed ground plane. Related research has also been done on conven- tional three-dimensional photonic crystals [38[42], but those between overlapping metal plates, as in Fig. 6. With this depend on different principles. Using high-impedance ground method, a capacitance of several picofarads is easily achiev- able. Resonance frequencies of less than I GHz can be of both the suppression of surface waves, and the unusual re- produced, while maintaining the thickness and period on flection phase. An antenna on a high-impedance ground plane the order of a few millimeters. However, by forcing a thin structure to have a low resonance frequency, the bandwidth produces a smoother radiation profile than a similar antenna on a conventional metal ground plane, with less power wasted in is also reduced the backward direction. Furthermore. radiating elements can The three-layer high-impedance surface maintains the same lie directly adjacent to the high-impedance surface without general properties as the two-layer structure, with TM and being shorted out. These antennas can take on a variety of TE surface-wave bands separated by a gap, within which forms, including straight wires to produce linear polarization, there are no propagating surface-wave modes. A surface-wave or various other shapes to generate circular polarizationPatch measurement is shown in Fig. 15(a) for a typical three-layer antennas are also improved if they are embedded in a high- structure. This sample had a hexagonal lattice with a period of impedance surface 6.35 mm, and an overlap area between adjacent metal plates of The high-impedance surface is particularly applicable to 6.84 mm2. The spacer layer between the plates had a thickness the field of portable hand-held communications, in which of 100 um, and a dielectric constant of 3.25. The thickness of the interaction between the antenna and the user can have the lower supporting board was 3. 17 mm, with a dielectric a significant impact on antenna performance. Using this new constant of 4.0. The data shows the transmission between two ground plane as a shield between the antenna and the user in straight coaxial probes lying parallel to the surface, in what portable communications equipment can lead to higher antenna is usually considered the TE configuration. The frequency is efficiency, longer battery life, and lower weight

2068 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 47, NO. 11, NOVEMBER 1999 (a) (b) Fig. 15. (a) Surface-wave transmission across a three-layer high-impedance surface. The lower resonance frequency is achieved through capacitive load￾ing. (b) Reflection phase of a three-layer high-impedance surface. If the desired resonance frequency is less than about 5 GHz, the thickness can be kept within reasonable limits by using three-layer construction, in which the capacitors are formed between overlapping metal plates, as in Fig. 6. With this method, a capacitance of several picofarads is easily achiev￾able. Resonance frequencies of less than 1 GHz can be produced, while maintaining the thickness and period on the order of a few millimeters. However, by forcing a thin structure to have a low resonance frequency, the bandwidth is also reduced. The three-layer high-impedance surface maintains the same general properties as the two-layer structure, with TM and TE surface-wave bands separated by a gap, within which there are no propagating surface-wave modes. A surface-wave measurement is shown in Fig. 15(a) for a typical three-layer structure. This sample had a hexagonal lattice with a period of 6.35 mm, and an overlap area between adjacent metal plates of 6.84 mm . The spacer layer between the plates had a thickness of 100 m, and a dielectric constant of 3.25. The thickness of the lower supporting board was 3.17 mm, with a dielectric constant of 4.0. The data shows the transmission between two straight coaxial probes lying parallel to the surface, in what is usually considered the TE configuration. The frequency is (a) (b) Fig. 16. (a) Antenna on a flat metal ground plane generates propagating surface currents, which cause multipath interference and backward radiation. (b) Surface waves are suppressed on a high-impedance ground plane. low enough that the free-space wavelength is much greater than the probe length, which is only a few millimeters, so the antennas tend to couple equally well to TM and TE modes. Transmission can be seen in both the TM and TE bands, and a gap is visible between 2.2–2.5 GHz. The reflection phase is shown in Fig. 15(b). The region corresponding to the surface-wave bandgap is shaded. Inside this gap, the reflection phase crosses through zero, and plane waves are reflected in-phase rather than out-of-phase. VII. ANTENNAS The high-impedance surface has proven useful as an antenna ground plane. Related research has also been done on conven￾tional three-dimensional photonic crystals [38]–[42], but those depend on different principles. Using high-impedance ground planes, antennas have been demonstrated that take advantage of both the suppression of surface waves, and the unusual re- flection phase. An antenna on a high-impedance ground plane produces a smoother radiation profile than a similar antenna on a conventional metal ground plane, with less power wasted in the backward direction. Furthermore, radiating elements can lie directly adjacent to the high-impedance surface without being shorted out. These antennas can take on a variety of forms, including straight wires to produce linear polarization, or various other shapes to generate circular polarization. Patch antennas are also improved if they are embedded in a high￾impedance surface. The high-impedance surface is particularly applicable to the field of portable hand-held communications, in which the interaction between the antenna and the user can have a significant impact on antenna performance. Using this new ground plane as a shield between the antenna and the user in portable communications equipment can lead to higher antenna efficiency, longer battery life, and lower weight